Anti-harmonic transformer

ABSTRACT

Devices for eliminating in a three-phase voltage transformer T, separating two networks A and B the voltage harmonics preexisting within the three phase voltage feeding A and detrimental to B, or the current harmonics generated by B and detrimental to A. The devices include single phase transformers, the primary windings of which are &#39;&#39;&#39;&#39;delta&#39;&#39;&#39;&#39; coupled and the secondary windings of which are &#39;&#39;&#39;&#39;star&#39;&#39;&#39;&#39; coupled, the angles determined by the legs of the triangles and of the stars exhibiting unique values, together with single phase autotransformers for connection to the A and B networks. When eliminating only current harmonics, T need only be constituted of two single phase transformers the primary secondary windings of which are in quadrature together with single phase transformers, the windings of which are connected to specific current taps provided on the above-mentioned transformers. They can be used in installations for electrochemistry, electrometallurgy, power distribution of d.c. current and for installations of static power conversion.

United States Patent Lys [54] ANTI-HARMONIC TRANSFORMER Jacques Francois MarieJoseph Lys, 3 bis Place Marquis 92, Clamart, France [22] Filed: Jan. 18,1971

[2]] Appl.No.: 107,048

[72} Inventor:

[30] Foreign Application Priority Data Jan. 19, 1970 France ..700l7l7 [52] U.S.Cl ..336/5, 321/57, 321/68, 323/48, 323/91, 336/12, 336/I80 [51] Int. Cl. ..H0li33/00 [58] Field oiSearch ..336/5, 10, 12, 170, 171, 180; 323/91, 48; 321/57, 58

[56] References Cited UNITED STATES PATENTS 1,227,415 5/1917 Fortescue ..336/12 2,975,357 3/1961 Manning .,..336/I2 X 2,989,685 6/1961 Kollmann ..336/l2 X FOREIGN PATENTS OR APPLICATIONS 160,887 12/1942 Germany ..336/l2 1 June 20, 1972 495,370 0/1938 GreatBritain.....'

..336/l 2 492,873 3/1930 Germany 12/ 127,635 9/1928 Switzerland ..336/ l 2 Primary Examiner-Thomas J. Kozma Attorney-Waters, Roditi, Schwartz & Nissen [57] ABSTRACT Devices for eliminating in a three-phase voltage transformer T, separating two networks A and B the voltage harmonics preexisting within the three phase voltage feeding A and detrimental to B, or the current harmonics generated by B and detrimental to A. The devices include single phase transformers, the primary windings of which are delta" coupled and the secondary windings of which are star" coupled, the angles determined by the legs of the triangles and of the stars exhibiting unique values, together with single phase autotransformers for connection to the A and B networks. When eliminating only current harmonics, T need only be con stituted of two single phase transformers the primary secondary windings of which are in quadrature together with single phase transformers, the windings of which are connected to specific current taps provided on the above-mentioned transformers. They can be used in installations for electroehemistry, electrometallurgy, power distribution of dc. current and for installations of static power conversion.

6 Claims, 11 Drawing Figures IGJ AG ML M B 5 H i C Bi (53 f PATENTEDJUHZO m2 3,671,901 sum 3 or 4 BACKGROUND OF THE INVENTION The present invention relates to polyphase voltage transformers for removing voltage and current harmonics from electrical networks which are connected by the transformers. For example, if the transformer separates a first from a second network with the power passing from the first to the second, it can protect the second network from the harmonics existing in the first network. Similarly, if the second network includes nonlinear elements which generate current harmonics, the present invention prevents such harmonics from being transferred to the first network.

In industrial practice, electrical polyphase voltage transformers are conventionally provided with symmetrical" windings whether or not they include single phase elements with independent circuits and star or polygon coupled electrical circuits, or include windings arranged on a single magnetic circuit with free or forced flux. They generally include a primary winding and a secondary winding for which are used conventional connection arrangements such as star", delta", mesh and so forth.

Depending upon the connection arrangements selected for the three-phase transformers, the third harmonics and their multiple can normally be eliminated. For instance, if both the primary and secondary windings are star coupled and their respective neutral points insulated, the fiux components produced by current third harmonics and their multiple are prevented from circulating. Moreover, if for example the 3 secondary winding is delta coupled, the electromotive force includes a frequency three times as high as the fundamental and generates in the delta circuit a current whose frequency is also triple, which almost completely suppresses the third harmonic and supplies the necessary ampere-toms for a correct compensation of the flux within the magnetic cores, whether the transformers are free or forced flux types.

This latter property is, furthermore, used more particularly for star-star coupled large transformers with delta arranged tertiary windings.

Therefore, in most cases only the third harmonics and their multiple are eliminated through the above mentioned conventional couplings.

SUMMARY OF THE INVENTION An object of the invention is to provide an improved apparatus for eliminating harmonics in single and polyphase BRIEF DESCRIPTION OF THE DRAWINGS FIGS. 1 and 2 are schematic diagrams of transformer couplings in accordance with this invention;

FIG. 3 is a geometric representation of the relationship between windings determined in accordance with this invention;

FIG. 4 is a schematic diagram of transformer windings geometrically arranged in accordance with this invention;

FIGS. 5 through 8 are schematic diagrams of geometric arrangements of transformers connected in accordance with this invention;

FIG. 9 is a geometric representation of the relationship between windings for eliminating voltage and current harmonies in accordance with the principles of this invention; and

FIGS. 10 and II are schematic diagrams of yet other windings geometrically arranged to eliminate voltage and current harmonics.

DETAILED DESCRIPTION With respect to the first above mentioned type, the present invention embodies with a three-phase system, a transformer 5 T made of two single phase transformers I and 2 the primary and secondary windings of which are electrically intercoupled in a "quadrature (see FIGS. 1 and 2).

The quadrature" coupling hereafter referred to is actually the coupling characterizing the three phase windings of the socalled Scott configuration, one of the windings having m times less winding turns than the other, and one of its ends being connected to the middle point of the other, both thus including the altitude and the base of an equilateral triangle, according to the classical conventional representation.

This quadrature" coupling for the couplings l and 2 has two possible arrangements: in the first, both transformers l and 2 have the same transfonnation ratio B equal to the transformation ratio of T; in the second, the transformers respectively have for a transformation B being the transformation ratio of T.

Transformers 1 and 2 are provided with intermediary current taps H and h on their respective windings and, between these taps, filtering" transfonners are provided.

According to FIG. 3 (related to the arrangement of FIG. I), the triangles ABC and abc have centers 0 and 0 which stand for the primary and secondary voltage triangles and their respective origins, two regular pentagonal contours centered in O and 0 can be formed having particular vertices A B C and 0 b,,, c,. These vertices are precisely carried by AH and BC for the first and by ah and be for the second transformer.

In accordance with transformer theory, the voltages across the terminals of a winding or part of it can be shown as the voltage diagram of the transformer and, similarly the segments shown as the diagram of voltages may represent the windings or part of windings at the terminals of which the voltages represented by these segments can be recovered.

Segments A,B,, A,C,, 0 b u e which are seen in FIG. 3, represent the windings of the single phase transformers linking v the unique points A,,, 8,, C,,, a b,, c

FIG. 4 is a diagrammatical representation of the device after both transformers have been arranged, the primary and secondary windings respectively connecting the unique taps bearing subscript 5. If a system of three phase sinuoidal voltages is applied to ABC, a system of voltages which are also three phase and sinuoidal will appear at abc; if moreover, the network fed in abc includes nonlinear impedances (rectifiers, thyristors or the like) the feeding currents will comprise, apart from the fundamental harmonics, all orders and, particularly, the fifth harmonics and their multiples.

The wound circuits A,B C and a b,,c,, taking into consideration the unique points or positions of the tap of subscript 5, have the property of only including, so far as currents with a frequency of five times the fundamental frequency is concerned, homopolar currents which are phase equal currents to which the impedance presented by A,B,C and a,b,c,, is very low.

In other tenns, the presence of the filtering" transformers (A585 a5b5) and (ASCS aScS) removes from the network the current harmonics of fifth order and their multiples. It is to be noted that removing a single phase transformer as (ASCS a5c5) does not change the result so that the fifth harmonic 70 which is sought to be eliminated can be completely suppressed by a single phase transformer with primary A 8, and secondary n b This result which has been shown for the fifth current harmonic can be extended to any harmonic of sequence i (i odd), the foregoing description applying to pentagonal con- 1 removed by embodying according to FIG. a filtering single phase transformer (Adi, tub respectively, at the level of the primary and secondary windings of the transformers 11 and 12, between. the intermediary taps A 8,, a -b the positions of which on the associated primary and secondary voltage diagrams are such that 0A, 08,, on, 0b, and the angles formed by CA, and OB, and 0a, and ob, are equal to a whole number of 2 11/1 radians. This condition can be written in accordance with the following expressions:

HAi ha, 1 1+ cos (2k+1)% HA it? 5 in which k is a whole number or null The geometrical segments thus outlined represent for the same coil the number of turns of the winding sections they stand for.

Using k 0, these expressions lead to a simple solution, viz.:

and without hindering the efficiency of the apparatus the presentation with k O'is more simple. tg is the trigonometric tangent.

Applying the same type of mathematical approach for the arrangement shown in FIG. 2 also allows removing current harmonics of sequence i. In fact, the transformer (A,B, a,b,) is arranged according to FIG. 6 between the taps A B, at the primary and ab, at the secondary winding; the tap b, extending from the winding b and the taps A B a b,, being so arranged that the triangles A,B H, and a,b,h,, with center 0, are geometrically similar and that 0a is equal to 0b,, it is possible under the same conditions as above to remove the harmonics of sequence i.

More specifically, the current taps A 8,, a,, b, between which the filtering transformer (A,B, o b is arranged are such (according to FIG. 6) that:

k being a whole number or null Without hampering the efficiency of the device, the representation of it is thus simplified.

One may note that the arrangements shown at FIGS. 5 and 6 extend to the harmonic of sequence i, the above mentioned property characterizing the delta coupled windings of conventional three phase transformers with respect to eliminating third order current harmonics and their multiple;

The anti-current harmonics" three phase transformer is thus characterized by the assembly of the two transformers 11-12 and 61 -62 and the associated single phase transformers (A 8, a,b,) as described hereabove.

This will eliminate all current harmonics of any sequence (generally odd) liable to be generated by nonlinear impedances fed from the network.

A balanced three-phase system is liable to cause theappearance of current harmonics of sequences 3,5,7,l 1,13,17,19, etc. each one susceptible to being eliminated by the method hereabove described. However, in order to embody the smallest possible number of single phase transformers one can limit the same, although sometimes with a slight efficiency drop of the device, to eliminate harmonics by units of 2. For instance the 5th and 7th harmonics can be substantially reduced through the embodiment of a single transformer (A 8, 11 b,) linking the taps A 8,, a b such according to the arrangement of FIG. 5

in replacement for the two transformers (A 3 a .,b and I (A B-,a,b,) theoretically required.

Similarly, the harmonics 11 and 13 could be substantially eliminated by the use of a single phase transformer linking the taps having the subscript l2, harmonics l7 and 19 being in turn eliminated by a single phase transformer of subscript l8 and so on.

Furthermore, for instance, harmonics l3 and 17 could be damped by a transformer linking the taps of subscript 15.

The geometrical segments thus outlined also represent for one Thus, and generally speaking, two harmonics following one another could be eliminated through a single phase transformer the subscript of which is equal to half the sequence sum of these harmonics. 7

It is obvious that this invention may apply to any polyphase system and is not restricted to three-phase systems; in particular, when the anti-current harmonic transformer also multiplies the number of phases.

FIG. 7 illustrates this property showingthe transformation of a conventional classical three phase system to a five-phase system: the transformer 71 comprises three windings, viz.: AH at the primary, a 11, and tab, at the secondary; the transformer 72 comprises two windings, viz.: BC at the primary and be at the secondary. Embodying suitable single phase transformers across the taps at the unique positions, according to the same principles as above outlined, allows eliminating current harmonics the number and the importance of which are reduced posed of single phase windings respectively arranged in quadrature. It is possible to utilize tertiary type windings wound as the above mentioned transformers 71 and 72 on the same magnetic circuits as the preceding ones and on which intermediary taps of the AB, and ab types are also provided; single phase transformers (A B, a,b,) link these taps in order to eliminate the current harmonics of sequence 1', this arrangementconstituting an extension of the principle of the transformers provided with three windings, one of which is delta arranged with a view toward eliminating harmonic 3.

The devices according to the second category'set forth at the beginning of the description enable voltage and currentharmonics of any i'sequence to be eliminated. They embody three single phasetransformers, as shown in FIG. 8, transformers which are 81, 82 and 83.

The transformer 81 is formed by a primary AB, and a secondary a,b,. The transformer 82 is formed by a primary AC, and a secondary up The transformer 83 is formed by a primary so, and secondary b,c,

The primary windings are delta coupled (dissymetrical) and the secondary are star coupled (also dissymetrical), with center 0. Feeding the primary windings A,B,C, occurs through autotransformers AH and BC which are themselves power supplied in A, B, C. Intermediary taps are provided on these autotransformers the position of which are such that:

as; (1 Ha 3 cos (2k+1-) Ir/ H B, H C, l F tg(2k+ 1) In these expressions k is a whole number or null and the outlined geometrical segments also characterize the modulus of the corresponding composite voltages.

The secondary windings are star coupled at and the end sections me, of the. star are, according to FIG; 8, connected by asingle phase transformer an; intermediary current taps b and c are provided on this autotransformer so that the end section b, of the star and the points b and 0 form an equilateral triangle, the center 0 of which is the same as that of the triangle a,b,c,. Similarly to the features of the devices described with relation to the first category, A B and C, represent the voltages at the diagram of FIG. 9 and, with relation to FIG. 8, the 3 particular vertices of a regular polygon having i sides cen tered in 0. The transformation ratios of transformers 81, 82 and 83 are:

as illustrated in FIG. 9.

The arrangement thus described is such that if the supply three phase voltage at A, B, C has a harmonic of sequence 1, the current harmonics of sequence i carried by the primary windings of transformers 8 1, 82 and 83 are homopolar, this meaning that they are equal and respectively in phase. Consequently, the harmonic three phase voltages of rank 1' at the secondary winding of transformers 81, 82 and 83 are in phase and those respectively available at the secondary winding of transformers 81, 82 and 83 are in phase and those respectively available at b,, b and c are equal with respect to modulus and phase. The composite voltages available across b b, c at the secondary winding are consequently free from any harmonic of rank 1'.

The present apparatus is reversible, this meaning that fed with athree-phase voltage at b,, b, c it will also exhibit at A, B, C a three-phase voltage free from any harmonics of rank i. Lastly, this arrangement can filter current harmonics of rank i in the same way as the devices of the above described first category. 1

Should several harmonics of the feeding voltage with ranks i, j I have to be eliminated, the above described arrangements for eliminating the harmonic i are applied one after the other and a series" arrangement is embodied which is characterized as follows:

Each harmonic can be eliminated through a set of three single phase transformers 81, 82 and 83, fed through adequate taps provided on the autotransformers AH and BC.

The secondary windings such as ca are series connected so as, one with the others the secondary windings such as or, and also the secondary windings such as 0b,. In that way, the primary windings of the type A,B, are parallel" arranged across the taps of the type A 8, set on All and BC whereas the secondary windings of the type ob, are series arranged in confonnity with FIG. 10; a single phase autotransformer is inserted between the end taps a and c of the secondary winding, and this single phase autotransformer is provided with intermediary current taps b and c in the same position as set forth above.

Consequently the three phase voltage available across the terminals b,, b, c is free from the harmonics of rank 1', j I that were to be eliminated.

This series" arrangement is likewise reversible and embodies 3n single phase transformers and three single phase autotransforrners, n being the number of harmonics of odd rank andof prime numbers with relation one to the other that were to be eliminated.

It is possible to simplfy the device by noting in FIG. 11 that the secondary current taps b and c can merge with the end taps a, and 0,, provided certain conditions are met: this will happen if certain current taps of the type A, are utilized exterior to the segment AH (see Fig. 11) so that the voltage triangle AB C, exhibits an obtuse angle greater than 2 1r/3 radians. Under such conditions, adequate transformation ratios can be selected and polygons ocp and oa can be built with the angle cpa, (FIG. 11) precisely equal to 2 1r/3 radians.

The devices according to the first category can'be used for all polyphase networks( generally three-phase) which have to be protected from the influence of current harmonics. This influence from harmonics is always a drawback and often causes power losses through eddy current, overheating, resonances and overvoltages, operation instability, radioelectrical disturbances and so forth. Apart from particular cases where eliminating a harmonic of any determined sequence is the main object, it should be noted that the anti-current harmonic" transformer can be used with'or without conversion of the number of phases before rectifiers and power thyristors: the current harmonics that the, latter often generate are detrimental in a general way to the network through which they are fed. Thisis the case for certain installations such as batteries charging, traction, electrochemistery, electrometallurgy, power supply for radio transmitters, power distribution through high voltage dc. current, and so forth.

The devices according to the second category can eliminate voltage and current harmonics. The anti-harmonics transformers thus defined are not only used for the application above-mentioned, but may also be used after certain generators supplying a periodical wave which is not purely sinuoidal such as inverters and static cycloconverters, particularly when those apparatus are assisted, that is when they feed an already existing network which commands frequency and voltage form.

What is claimed is:

1. Apparatus for eliminating harmonics comprising a transformer coupling a first network to a second network, said transformer comprising two single phase transformers including respective primary windings connected in quadrature and respective secondary windings connected in quadrature, said primary windings being electrically connected together by connecting one end of one of said primary windings to a tap point on the other of said respective primary winding, said secondary windings each being electrically connected to a tap point on the other of said respective secondary windings, said tap points being located at the midpoints of said other of said respective primary and secondary windings, said primary windings having 3/2 times the number of turns of said respective secondary windings, said primary and secondary windings being provided with intermediary taps designated A, and B, on said primary windings and a, and b, on said secondary windings, the subscript i representing the odd harmonic to be eliminated, the positions of said taps being defined as:

wherein k is a whole number or null and the designated geometrical segments represent the number of associated winding turns and H and h are the midpoint taps of said respective primary and secondary windings; and two further single phase transformers including primary and secondary windings and having a transformation ratio B, the primary windings and secondary windings of said two further single phase transformers being arranged across the taps A, and 8,, and a, and b. respectively.

2. Apparatus according to claim 1 wherein said apparatus comprises a three phase transformer having a transformation ratio B comprising two single phase transformers electrically coupled together, the respective primary windings of said single phase transformers being electrically connected together by connecting one end of said primary of one of said single phase transformers to the midpoint of the other primary, said midpoint being designated as H, the respective secondary windings of said single phase transformers being electrically coupled together by connecting one end of the secondary of the other of said single phase transformers to the midpoint of the secondary of said one of said single phase transformers, said latter midpoint being designated h, N and n designating the number of winding turns of the primary and secondary windings of said one of said single phase transformers and N and n the number of winding turns of the primary and secondary windings of said other of said single phase transformers, the transformation ratios )9, and ,8: if said single phase transformers being:

wherein k has simultaneously the same value andin which the designated geometrical segments represent winding parts and for one same coil the number of winding turns of the winding portions they stand for; the primary and secondary windings of at least one of said further single phase transformers having a transformation ration of 3. Apparatus according to claim 1 wherein the parameter k is null and the subscript i is equal to half the sequence sum of the two following harmonics which are to be eliminated.

4. Apparatus according to claim 2 wherein the parameter k is null and the subscript i is equal to half the sequence sum of the two following harmonics to be eliminated.

5. Apparatus for eliminating harmonics comprising (a) first and second autotransformers respectively designated AH and BC, said autotransformers being electrically connected togetherwith a connection of one end of autotransformer AH to the midpoint H of the second autotransformer BC, a current tap A. on said autotransformer AH, a pair of current taps B, and C, on said autotransformer BC, (b) three single phase transformers including primary windings designated A,B,, ac, and GA, current taps A,, B C being coupled in accordance with the following relationship:

wherein k is a whose number or null and in which the designated geometrical segments represents the number of turns of the associated winding sections, the secondary windings of said single phase transformer being designated 1gb, Inc, and 0,0, and respectively conforming to the following relationship: 

1. Apparatus for eliminating harmonics comprising a transformer coupling a first network to a second network, said transformer comprising two single phase transformers including respective primary windings connected in quadrature and respective secondary windings connected in quadrature, said primary windings being electrically connected together by connecting one end of one of said primary windings to a tap point on the other of said respective primary winding, said secondary windings each being electrically connected to a tap point on the other of said respective secondary windings, said tap points being located at the midpoints of said other of said respective primary and secondary windings, said primary windings having square root 3/2 times the number of turns of said respective secondary windings, said primary and secondary windings being provided with intermediary taps designated Ai and Bi on said primary windings and ai and bi on said secondary windings, the subscript i representing the odd harmonic to be eliminated, the positions of said taps being defined as: wherein k is a whole number or null and the designated geometrical segments represent the number of associated winding turns and H and h are the midpoint taps of said respective primary and secondary windings; and two further single phase transformers including primary and secondary windings and having a transformation ratio Beta , the primary windings and secondary windings of said two further single phase transformers being arranged across the taps Ai and Bi, and ai and bi respectively.
 2. Apparatus according to claim 1 wherein said apparatus comprises a three phase transformer having a transformation ratio Beta comprising two single phase transformers electrically coupled together, the respective primary windings of said single phase transformers being electrically connected together by connecting one end of said primary of one of said single phase transformers to the midpoint of the other primary, said midpoint being designated as H, the respective secondary windings of said single phase transformers being electrically coupled together by connecting one end of the secondary of the other of said single phase transformers to the midpoint of the secondary of said one of said single phase transformers, said latter midpoint being designated h, N1 and n1 designating the number of winding turns of the primary and secondary windings of said one of said single phase transformers and N2 and n2 the number of winding turns of the primary and secondary windings of said other of said single phase transformers, the transformation ratios Beta 1 and Beta 2 of said single phase transformers being: the primary and secondary windings of at least one of said further single phase transformers having a transformation ration of
 3. Apparatus according to claim 1 wherein the parameter k is null and the subscript i is equal to half the sequence sum of the two following harmonics which are to be eliminated.
 4. Apparatus according to claim 2 wherein the parameter k is null and the subscript i is equal to half the sequence sum of the two following harmonics to be eliminated.
 5. Apparatus for eliminating harmonics comprising (a) first and second autotransformers respectively designated AH and BC, said autotransformers being electrically connected together with a connection of one end of autotransformer AH to the midpoint H of the second autotransformer BC, a current tap Ai on said autotransformer AH, a pair of current taps Bi and Ci on said autotraNsformer BC, (b) three single phase transformers including primary windings designated AiBi, BiCi, and CiAi , current taps Ai, Bi, Ci being coupled in accordance with the following relationship: wherein k is a whole number or null and in which the designated geometrical segments represent the number of turns of the associated winding sections, the secondary windings of said single phase transformer being designated aibi, bici and ciai and respectively conforming to the following relationship: and being coupled in a star configuration, (c) a further single phase autotransformer aici including intermediary current taps b and c for connecting the second network.
 6. Apparatus for eliminating harmonics as claimed in claim 5 comprising 3n single phase transformers for eliminating n harmonics of order i, j . . . 1, said 3n single phase transformers being series connected to said three single phase autotransformers. 